- Title
- Canonical dual approach for minimizing a nonconvex quadratic function over a sphere
- Creator
- Chen, Yi; Gao, David
- Date
- 2013
- Type
- Text; Conference paper
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/81622
- Identifier
- vital:8243
- Identifier
-
https://doi.org/10.1007/978-3-319-08377-3_16
- Identifier
- ISBN:21941009 (ISSN); 9783319083766 (ISBN)
- Abstract
- In this paper, we study global optimal solutions of minimizing a nonconvex quadratic function subject to a sphere constraint. The main challenge is to solve the problem when it has multiple global solutions on the boundary of the sphere, which is called hard case. By canonical duality theory, a concave maximization problem is formulated, which is one-dimensional and without duality gaps to the primal problem. Then sufficient and necessary conditions are provided to identify whether the problem is in the hard case or not. A perturbation method and associated algorithms are proposed to solve hard-case problems. Theoretical results and methods are verified by numerical examples. © Springer International Publishing Switzerland 2015.
- Publisher
- Springer New York LLC
- Relation
- 3rd World Congress on Global Optimization in Engineering and Science, WCGO 2013; Anhui, China; 8th-12th July 2013 Vol. 95, p. 149-156
- Rights
- Copyright © Springer International Publishing Switzerland
- Rights
- This metadata is freely available under a CCO license
- Subject
- Canonical duality theory; Global optimization; Quadratic minimization problems; Trust region subproblem; Numerical methods; Perturbation techniques; Spheres; Canonical duality theories; Global optimal solutions; Maximization problem; Perturbation method; Quadratic function; Quadratic minimization; Sufficient and necessary condition; Problem solving
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